The field of this invention relates to devices that produce useful work from wind energy, and more specifically devices that extract energy from the wind using tethered kite structures.
Collecting energy from the wind has been well know for more than 1000 years. However, nearly all wind energy has been collected near the ground. In recent years several designs have been proposed to take advantage of wind at higher elevation. The advantage of using high elevation wind is two-fold. First, wind speed is greater because boundary layer effects at the surface have less effect at high elevation. Second, there is a much greater volume of air flowing above 300 feet than below this elevation. In general, wind speeds increase with increasing elevation, however, the relationship is not always stable and can be much higher at night due to uncoupling of the air stream. According to the National Weather Service, average wind speed in the US is three times faster at 853 feet than at 15 feet.
Estimating total wind energy is difficult because not all available wind is economical to capture, plus, there is no consensus from the scientific community on exactly how much total available wind energy there is. Estimates of total wind energy is placed somewhere between 0.25 percent and 3.0 percent of the total solar radiation intercepted by the earth (Solar total=1018 kWh/year, 1% Solar Total=1016 kWh/yr). It is estimated that a practical wind energy of 20xc3x971012 kWh/year could be recovered over strategic land areas, and would represent a 4% land utility and 23% capacity factor for standard wind turbines. This translates into a savings of 100 million barrels of oil per day, should all this potential be exploited. The proposed Lift-Mode Linear Wind Turbine (or simply Linear Turbine or Lift Turbine), has far more wind energy available to it than a standard wind turbine. This is because can it operate economically in very low wind speeds, and can collect energy from the wind well above 300 feet elevation, and possibly to 3,000 feet, with similar heights over water. Since wind energy increases with the cube of air speed, higher elevation wind would have a much greater mean energy density than wind near the ground, and have a much greater volume of air available to it. The Linear Turbine is also well suited to operation at sea because of its low center of gravity and very low turning moment. The result is that wind energy available to a Linear Turbine is enormous. For comparison, world energy usage is 400xc3x971015 Btu per year or about 1.2xc3x971014 kWh/year including coal, oil, and gas. A conservative estimate of wind energy available between 300 and 3,000 feet elevation is 1015 kWh/year or about 10% of the total available wind energy. Most of this wind is high energy density (above 300 W/m2), and viscose interactions within the air flow would allow drag effects to recover wind energy well above 3,000 feet as multiple systems slow the entire air stream. If 10% of this available energy was recovered (1014 kWh/yr), there would be enough energy to displace nearly all current world energy usage.
The linear wind-turbine disclosed here has many advantages over all other wind generation system. The power density of the disclosed invention is over a hundred times greater than other prior art self-erecting wind energy systems. Systems such as those disclosed by inventors Carpenter, Lois, Loeb, Ockels, and Payne all operate at below ambient wind speed, and would produce 100 times less power than the Applicant""s linear wind-turbine of similar size. Though the high-speed systems disclosed by Loyd and Payne use high-speed flight to capture wind energy, they do it in such a way that makes them unworkable by placing large-complicated machinery in its air vehicle or using pulley systems that make control nearly impossible.
The Applicant""s linear wind-turbine system operates under novel physical principles and is the only known example of a greater-than-ambient-wind-speed energy device that collects wind energy by movement in the AXIAL direction. The AXIAL direction being defined as the direction perpendicular to the airfoil""s flight direction (not including the AXIAL movement itself), in the same plane as the LIFT and DRAG force vectors. For the special case where the airfoils rotate about a fixed point (see ground station 30 in FIG. 2), the AXIAL direction is in the same direction as the radial vector in spherical coordinates with its vertex centered at the fixed point (pivot point of control lines in ground station 30). For other non-spherical systems, such as Payne""s design U.S. Pat. No. 3,987,987, the AXIAL component is simply the component of LIFT perpendicular to the airfoil""s flight path which does no work in Payne""s design. AXIAL wind-turbines represent a completely new way of collecting wind energy. The combination of AXIAL energy collection and high-speed operation, provide the linear wind-turbine system with advantages that no other system can match, i.e. extremely light-weight devices, simple flight controls, and very-high power density.
Snow and ice would stop any low power wind kite system, but the disclosed design has the high power density that can handle nearly any adverse weather. Other advantages include high elevation operation which makes available the collection of energy from a much larger percentage of the total wind energy on Earth. Expensive components of the Linear turbine remain on the ground and protected, only the airfoils are exposed, with all heavy components of the system placed on the ground. This allows buoyant airfoils to be used. Also, because of the very low center of gravity for the system, it can easily be placed at sea with the addition of a few control systems to compensate for the added rocking motion of the platform due to waves. Since the control system is already designed to handle a wide range of control line movement, making the flight control system insensitive to rocking and rolling of the ground station (sea station) is relatively straightforward. The design allows easy lowering the buoyant kites by either reeling them in or by controllably flying the kites to the ground for easy replacement or repair.
Many lighter-than-airships have been proposed for collecting this energy; but lifting an entire windmill and generator into the sky is expensive at best. These large airships are also susceptible to damage even in mildly strong winds making this type of system an extremely uneconomical method of collecting the wind energy.
Lois U.S. Pat. Nos. 3,924,827 and 4,076,190, Loeb U.S. Pat. No. 4,124,182, and Carpenter U.S. Pat. No. 6,254,034 B1 disclose devices for collecting wind energy using airfoil wings which produce drag for playing in and out a line attached to a pulley. While these inventions look similar to the Applicants invention, they are in fact missing key structures needed to allow the approximately 100 fold increase in power density that the Applicant""s invention provides. Lois, Loeb and Carpenter use drag wind force on the kites (airfoil, wing, aircraft) to produce power, with lift coming from wind flowing around the kite. Lois, Loeb and Carpenter all realize maximum power at kite speeds equal to approximately one-third the wind velocity. These kite designs operate due to drag forces from direct wind resistance created by the wing. This operating criteria greatly limit the amount of energy collected because the kite must move generally in the direction of the wind. Carpenters design attempts to maximizes this drag by placing the airfoil (aircraft) at an angle-of-attack just beyond aerodynamic stall where turbulent airflow around the kite (aircraft) would create significant drag (called lift by Carpenter) to force the kite to move downwind. The Applicants invention on the other hand operates the airfoil (kite) at high-speed, with its airfoil moving substantially perpendicular to the wind stream (Lois, Loeb and Carpenter all have the kite move generally parallel to the wind stream). This high-speed operation allows the airfoil to interact with wind energy over a very large area, thus collecting many times the energy that Lois, Loeb or Carpenter""s wing could ever hope to collect. For Lois, Loeb, or Carpenter""s invention to operate like the Applicants, they would have to modify their kite design to have: 1) a high lift-to-drag (L/D) ratio; something that would lower the efficiency of Lois""s and Carpenter""s designs since they both rely on drag for power, 2) a means to make the wing operate at high-speeds (significantly above the ambient wind speed), and 3) a means to control the flight-path of the kite as it moves perpendicular to the wind at high-speed. Lois, Loeb, and Carpenter instead shows a slow-speed (slower than wind speed) wind energy device that uses DRAG to produce power, but does not control the wing to induce high-speed flight, or flight perpendicular to the wind. The result is that Lois, Loeb, and Carpenter realize a power density (power generated per unit wing area) of less than {fraction (1/100)}th that of the Applicant""s design. That is, the Applicant""s design can produce over 100 times the power for a given kite size and wind speed, than Lois, Loeb, and Carpenter""s designs can.
All wings produce aerodynamic forces when moved through the air. These forces are spread across the entire surface of the airfoil and very in both direction and intensity for any given section of the airfoil. For simplicity all these forces are summed together and represented by a vector that goes through the center of moment of the forces on the airfoil. In practice, this single force vector is rarely used, but is instead broken into 2 perpendicular components, one called LIFT and the other called DRAG. In FIG. 1 we see, a schematic of the force vectors on an airfoil. The LIFT force is defined as the force on the airfoil perpendicular to the apparent airflow direction, and DRAG is defined as the force on the airfoil in the direction of the apparent airflow direction (effective wind direction). These LIFT and DRAG force vectors are chosen for convenience of calculating forces, and can be redistributed in other directions to allow calculating other factors of the airfoil. For example, the LIFT force component can be broken into an AXIAL force component (perpendicular to direction of travel) and a THRUST component (in the direction of travel). Since all high-speed wind turbines use the THRUST component of the forces to generate power this is an important force vector to know. The AXIAL force vector is also important to know since it represents the force that must be resisted to keep a standard wind turbine from blowing away.
For the disclose invention, this AXIAL force is equal and opposite to the control line tension. It is this control line tension that produces the useful power. As the line is forcefully reeled out, it turns a pulley that turns a generator to produce electrical power. Since the control lines are perpendicular to the THRUST force, the airfoil is allowed to move freely in the direction of THRUST. After the airfoil reaches maximum speed, the DRAG on the unrestrained airfoil kite exactly cancels the THRUST component in steady-state flight. Thus, for the disclosed invention, all THRUST is used to either accelerate the airfoil or is dissipated by air DRAG force. On high LIFT-to-DRAG ratio airfoils, the AXIAL force vector is numerically and directionally nearly the same as the LIFT vector and will at times in this discussion be used interchangeably. For L/D=10 the AXIAL and LIFT vectors are only 5.7 degrees (xcex1=5.7xc2x0) apart when the airfoil is in steady-state flight. The angle-of-attack is defined as the angle between the chord line (line between the leading edge of the airfoil and the trailing edge of the airfoil), and the apparent wind direction. For this special case where THRUST and DRAG cancel, the angle-of-attack depends heavily on the lift-to-drag ratio of the airfoil, and for L/D=10 is equal to 5.7 degrees. This means that for the airfoil in FIG. 1, the chord line lies in the airfoil""s direction of flight (or airfoil pitch angle equal to zero). Where airfoil pitch angle is defined as the angle between a plane perpendicular to the control line axis (direction of travel when not being reeled in or out) and the chord line of the airfoil.
The Applicants invention is the only known example of a wind energy collector where a high-speed airfoil is used to produce power through the AXIAL component of the aerodynamic forces on an airfoil. All other high-speed wind turbines and wind energy devices use the THRUST component of the airfoil""s aerodynamic force to create power output. For example, on a standard wind turbine (spinning propeller), the rotor blades turn on an axis that is parallel with the wind. Thus, the blade""s tips move perpendicular to the wind at very high speed and the AXIAL force component on the blades points directly downwind. This AXIAL force is resisted by the attachment of the rotor hub to a tower or other support. The THRUST component points in the direction of rotation for the blades, and produces the rotational force (torque) that turns the blades to produce power. All known wind energy systems which use high-speed airfoils to produce power, only use the THRUST component of their airfoils to generate power. Below are a few examples of such THRUST driven wind energy systems.
U.S. Pat. No. 3,987,987 to Payne is an example of a THRUST driven wind energy system. In FIG. 1a of his patent, we see Payne""s typical design. A single line is attached through two pulleys with both ends attached to the wing (airplane). The nature of the system is that the wing is constrained by the continuous line to follow a parabolic path in the sky. Unless the line goes slack or the line is broken, the wing""s flight direction must follow this parabolic path. All forces perpendicular to the flight path (AXIAL) are restrained by the line and pulleys. Thus, only the THRUST component on the wing (in the direction of flight), produces a differential tension on the two ends of the line to transfer useful energy to the ground. The Applicant""s design on the other hand collects none of the energy produced by the THRUST and instead uses all THRUST to overcome air drag on the wing (airfoil kite) for high-speed flight. Power is instead collected by the letting-out of the tether line under the force created by AXIAL forces (LIFT) on the airfoil. The tether by its flexible nature can only exert a force along its length. Thus, only the AXIAL component which is in-line with the axis of the tether can transmit force to the ground and thus generate power. Payne""s system, however, uses only the THRUST component to produce power, which is perpendicular to the AXIAL component used by the Applicant. Payne also uses airplane like controls to control the flight path of the airplane. This adds bulk to the airborne portion of the system and makes it more difficult to keep aloft. Payne does elude to the use of kite type controls but gives no examples, only saying they are common. This is true for kites with fixed lines connected to a static point on the ground, but it is completely unknown technology on how to control a kite that varies in distance from any given point on the ground. Since the kite would follow a parabolic path, their is no central axis where static control lines can be positioned, thus any control from the ground would have to be able to adjust not only for changing distance from the kite, but also changing angles of flight path with respect to the ground controller. Such controls are still an unknown. So while Panye shows a parafoil kite for use in his system, he neither shows a means of accomplishing this, nor is their any prior art that could easily allow him to control the parafoil under such conditions.
This application discloses how to make a control system for controlling an airfoil shaped kite with a changing tether length. The technical requirements for the disclosed system are less complicated than Panye""s design which would need to control multiple changing axis in its flight path. For example, because the applicant""s design follows a generally spherical flight path there is no need to have to adjust the pitch angle (angle between the chord line of the airfoil and a plane perpendicular to the control line axis) with respect to the tether control lines (Panye""s design does not have this luxury), because the airfoil is always flying perpendicular to the tether. Minor changes in airfoil""s angle-of-attack can be added to provide even higher efficiency by compensating for the small changes in apparent air flow direction. These changes in airflow direction can be the result of many factors such as air turbulence, direction of flight of the airfoil, speed of the airfoil, relative motion of the airfoil with respect to wind direction, and etc. The disclosed system teaches a means of controlling all these factors by controlling the angle-of-attack (and pitch angle) of the airfoil.
U.S. Pat. No. 6,072,245 to Ockels shows a wind energy system which uses multiple airfoil wings to generate power. This design uses aerodynamic THRUST to produce power, and only operates the wings at less than ambient wind speed. The wing""s leading edge is pointed substantially into the wind during operation. At first glance one may think that Ockels"" design uses the lift on the wings to produce power, however, by definition, THRUST is the force component in the direction of motion of the aerodynamic wing. In Ockels case, the wings can only move along the path described by the cables connecting the wings, and thus by definition, only the THRUST component on the wings do useful work. The AXIAL component (force perpendicular to the THRUST) is restrained by Ockels"" cabling structure and does no work. Because of this, Ockels device is very limited in the power it can generate from a given wing area. The Applicant""s design in contrast uses a airfoil surface that points its leading edge substantially perpendicular to the wind creating useful force in the general direction of the wind, not perpendicular to it. From this point alone one can see that the Applicant""s and Ockels"" devices operate under completely different physical conditions, and produce completely different levels of power output. The applicant""s device may be operated at air speeds greater than 6 times the ambient wind speed. Since power in an airflow goes up as the cube of the airflow speed the Applicant""s device will be interacting with air having an energy density 216 times (63) that of Ockels. Granted not all this energy is available for extraction, but neither is all the wind energy striking Ockels design at ambient wind speed available for extraction. Thus, all other factors being equal, the Applicant""s design can generate over 100 times the power as a similarly sized airfoil using Ockels"" design.
U.S. Pat. No. 4,251,040 to Loyd is another example of a THRUST driven wind energy system. In this case the thrust generated by a winged aircraft propel the aircraft at high-speed through the air. This high-speed flight is then used to drive propellers on the aircraft to produce useful power which is transmitted to the ground. The power generated by the propellers is taken directly from the forward motion of the aircraft in the form of drag. Thus, the power generated by the THRUST of the plane is collected by the propellers. The AXIAL force component on the wings of the aircraft is constrained by the cables connecting it to the ground and is not used to produce power. The Applicant""s device, as mentioned before, operates exactly opposite Loyd""s design using the AXIAL component to produce useful power and throwing away the energy generated by the THRUST component. By using the AXIAL forces instead of THRUST forces to produce power allows all the heavy linkages, propellers, and transmissions that Loyd uses, to be eliminated from the air-born portion of the design. This has many advantage which include making the system much lighter and easier to keep air-born. In fact, by eliminating these components the airfoil can be made so light that using an airfoil inflated with a lighter-than-air gas can allow the airfoil to actually be lighter-than-air. A buoyant airfoil has many advantages, one being that it can stay aloft even with no wind.
Linear Wind-Turbine Physics
Consider a typical wind turbine rated at one megawatt. It would have a 50 meter diameter rotor with two blades, reach a peak power at a wind speed of 15 m/s, and cutting off at 25 m/s. If we consider the outer 10 meters of each blade we find that these two small blade tips sweep out 64 percent of the turbine""s area, and produce roughly 90% of the power output. Now consider removing these blade tips from the blades and discarding the remainder of the blades, its rotor hub, the nacelle, and the tower (representing 57.5% to 73% of total turbine cost, including land costs), and replacing all this with a system of inexpensive cables. These cables allow the blade tips (or airfoils) to operate in a linear fashion, and at higher elevations ( greater than 300 feet) where the power density of the wind is much greater. Furthermore, because the airfoil tips are not constrained to a circular path, they do not have the limited area of wind capture, increasing line length increases the collection area, thus sweeping a large area at high speed, and intercepting undisturbed air. The result is a system that has the potential to produce the same power, but at a lower wind speed, and at a much lower initial capital cost.
Linear Wind-Turbine System
The disclosed invention uses light-weight durable flexible airfoils operating at high lift-to-drag ratios and high speed. The airfoils are placed at the end of Control Lines (tethers) which are attached to a ground station (see FIG. 2). These Control Lines allow the airfoils to operate much like a high performance, controllable, stunt kite, except the control lines can be extended to collect power and retracted to repeat the process. At the end of each extension (power stroke) of the control lines, the airfoils are tilted toward the wind (airfoil pitch angle negative) to easily retract (rewind) the airfoil for the next power stroke. The high-speed flight of these airfoils can produce power levels similar to those experienced by large wind turbine rotor blades, except the airfoil kite would always experience full free stream wind speed, which would offsets any loss of efficiency due to improper orientation of the airfoil when it is not exactly perpendicular to the wind flow direction. Energy is collected from the fast moving airflow by allowing the airfoil""s control lines to be reeled-out (played out) under the high tension (AXIAL force) on the lines. A pulley converts this linear motion into rotary power which is transmitted to an electric generator or other energy transmitting device, such as an air compressor, pump, etc. Thus, the control lines serve three purposes: 1) to support the airfoil""s lift (AXIAL force), 2) to provide flight and lift control over the airfoil, and 3) to transmit power to the ground.
The art of controlling a self-erecting airfoil kite is well known with several different existing methods, two of which are dual or quad control line configurations. In FIG. 2 we see a Quad-line controlled airfoil. Such control schemes are used in present day high performance stunt kites. Quad-line control has the advantage that the angle-of-attack can constantly be controlled to optimization of power collection, to make adjustments for wind gusts, and to reduce power output in high wind conditions. The standard quad control line configurations must be modified for use here because the length of the control lines will not be static. Instead the lines will reel in and out so that useful power may be extracted from them. Such a control system is novel and will be described later in this discussion. The quad control line configuration places one control line near each of the four corners of the airfoil. A rigid spar is often used to support the airfoil, but in this design the pressurized airfoil tends to support itself, and support lines are added to assure the airfoil holds its shape. By changing the length. of the lines on the front and back of the airfoil, the pitch angle and angle-of-attack of the airfoil can be controlled. If the pitch angle on one side of the airfoil is reduced and the other remains the same, then the additional drag on that side will change causing a differential THRUST (and LIFT and pitch angle) on the two ends of the airfoil and will cause it to turn in flight. By this method the LIFT and flight path of the airfoil can be controlled by adjusting the length of the control lines to provide the proper airfoil angle. Being able to control the angle-of-attack also allows the airfoil to be throttled back in high winds. This is a great advantage because too much generated power can break the control lines or damage the airfoil. Quad line control allows the Linear Turbine system to remain operational over a much greater range of wind speeds and conditions than a standard wind turbine. The normal operating speed for the airfoil will be from 50 to 180 miles per hour. Thus, even wind speeds of 180 mph pose only minor problems for this system because the airfoil can be flown stationary in the sky and experience approximately the same forces as if it were sweeping across the sky at 180 mph in a 30 mph wind. To do this the airfoil must quickly adjust to high gust forces by changing its angle-of-attack, which can be accomplished by any one of a number of force control means like the quad-line configuration described above. Note that the stretch in the tether line itself will absorb some of the energy generated by wind gusts. Also the control lines can be let out more quickly to reduce the effective wind speed the airfoil experiences, thus reducing the forces.
Before we go into great detail of the preferred embodiments, we should consider some of the physical properties involved which govern the operation of this type of turbine kite system. At this time it is sufficient to understand the general design for the turbine kite from FIG. 2. This system consists of three airfoil kites 50 in tandem which are attached to the Ground Station 30 by support lines 60L and 60R, and control lines 58L and 58R (collectively the support lines and control lines will be referred to throughout this patent as control lines). By controlling the differential length of these control lines, the airfoil""s direction and speed can be controlled from the ground to follow the shown Flight Path. The control lines are also directly connected to a shaft and pulley system (see FIG. 12) in the Ground Station 30. As the Airfoil Kites 50 are propelled by the wind at very high speed, all four control lines are reeled-out under tremendous force causing the pulley and shaft in the Ground Station to turn a generator to generate electricity. The LIFT on the airfoil is linearly proportional to the power output of the airfoil, the more LIFT the more power. After the Airfoil Kites have made their: Power Stroke, the airfoil""s pitch angle is made negative (pointing the leading edge into the wind) which immediately changes the angle-of-attack and slows the airfoil. The airfoil can now be reeled back in by the control lines with a minimum of force. Once the airfoil has been rewound to the proper place, the airfoils are again angled to generate powerful AXIAL LIFT. This process repeats over and over again to produce power. Since the force to rewind the airfoils is much less than the force generated during reel-out, there is net power generated.
The Linear Wind-Turbine system in FIG. 2 can be controlled through the cables coming from the ground station with two support lines 60L and 60R in the front, and two control lines 58L and 58R in the rear. While all four lines can be used to control the airfoil, it is generally sufficient to use just the two rear control lines 58L and 58R to adjust pitch angle and angle-of-attack. By adjusting the length of the control lines in the rear with respect to the support lines at the front, the airfoil""s flight path can be controlled from the ground through differential drag caused by a different angle-of-attack on each side of the airfoil. Note that for an operational system all the lines may be bunched together in a single conduit between the airfoil and the ground station. The single conduit would reduce air drag on the lines, but would also add weight. There are many other methods available for control of the airfoil, but this one works well for present kite technology, and allows for quick adjustments in the pitch angle. The control lines constrain the lift generated by the airfoils and transmit most of the power to the ground station through an oscillating playing in, and out, of the support lines 60L and 60R, and control lines 58L and 58R (control lines). As the airfoils are propelled forward at high speed by the wind, the airfoil experiences LIFT. This LIFT causes the control lines to reel-out and turn a pulley- system on the ground, thereby transferring energy to the ground to generate electricity. Because of the slow turning rate of the pulley, a transmission may be needed between the pulley and the generator. A pulley and transmission in the Ground Station would be used to turn a generator. Power conditioning circuits would generate 60 Hz electricity from the generator""s output. If two or more separate airfoil kites are connected mechanically they can be sequenced to produce their power stroke in succession providing relatively smooth turning of the pulley and generator. In this case, a synchronous generator may be used. Control for the generator""s rotation speed would come from feedback to the generator which would control the turning rate of the pulley by electronically controlling the torque being generated by the generator. As torque increases on the pulley, the generator would increase its winding field strength to increase power output and keep the rotational speed constant. As torque decreases, the winding field strength would be reduced to allow the generator and pulley to rotate more easily to maintain its constant rotation rate. Thus, for a synchronous generator the play-out of the tether cables would always be at the same speed. This means that efficiency would be reduced because the power output is maximum at reel-out speeds of ⅓ the wind velocity. However, as we will see in the following text, this loss is relatively small over a fairly large range. Synchronous generator can also have two or more operating speeds to improve efficiency. Also, multiple gear ratio transmissions can be use used to help keep the control line power stroke speed near the range for maximum efficiency.
On very windy days the Linear Turbine may reach its maximum power. When this happens something must be done to reduce the power generated by the airfoil. A number of things can be done to reduce power. One is to simply changing the pitch angle of the airfoil as wind speeds increase. By changing the airfoil pitch angle with the control lines, the airfoil speed can be reduced to limit the output power of the airfoil. Another way to reduce power is to have the airfoils tack back and forth more closely near the zenith (vertical above the ground station). This causes the wind to hit the airfoil at a greater and greater glancing angle, thus reducing power collection by the factor Cos3(xcex8), where xcex8 is the angle between the wind direction and the longitudinal axis of the control lines at the airfoil. Power can also be controlled by using a combination of airfoil""s pitch angle and changes in the xcex8 angle. Eventually, at very high winds, over 120 MPH, the airfoil would remain nearly vertical above the power station, and simply oscillate up and down to produce power. The Linear Turbine would still be producing near maximum power as it tacked up and down in the 120+MPH wind. However, care must be taken not to loose control of the airfoil in these high wind conditions.
Energy and Power Physics
The power in an incompressible fluid flow has been shown to be proportional to the cube of the flow velocity. This makes sense when we consider the kinetic energy of an air flowing mass through an area A with velocity U.
Wind Power=xc2xdxcfx81U3Axe2x80x83xe2x80x83Eq. 1
Lift=L=xc2xdxcfx81Vr2CLAxe2x80x83xe2x80x83Eq. 2
Drag=D=xc2xdxcfx81Vr2CDAxe2x80x83xe2x80x83Eq. 3
Where,
xcfx81=Ambient air density
U=Free stream Wind Velocity at airfoil
A=Projected Area of airfoil
Vr=Airfoil""s resultant air velocity
Analysis of an airfoil as a free translating body yields the power extracted as:
PFoil=xc2xdxcfx81U3A(v/U)[CLxe2x88x92CD(v/U)][1+(v/U)2]xc2xdxe2x80x83xe2x80x83Eq. 4
Where,
v=Velocity of airfoil
CL=Lift coefficient≈1.0
CD=Drag coefficient≈0.1
CP=Power Coefficient
L/D=Lift-to-Drag ratio≈10
It can be shown that maximum power occurs at v/U=(2/3)CL/CD (i.e. 2/3 of the Lift-to-Drag ratio) for a lifting body. This 2/3 factor is true whether the power is being extracted by dragging a wind turbine behind the airfoil, or power is being extracted by the forceful playing out of the tether control lines. In either case, the maximum power coefficient for an airfoil translating at a right angle to the wind can be found from Equation 4 by substituting (2/3)CL/CD in for v/U:                                                                         C                                  P                  ,                  max                                            =                                                (                                      2                    /                    9                                    )                                ⁢                                                                                                    C                        L                                            ⁡                                              (                                                                              C                            L                                                    /                                                      C                            D                                                                          )                                                              ⁡                                          [                                              1                        +                                                                              (                                                          4                              /                              9                                                        )                                                    ⁢                                                                                    (                                                                                                C                                  L                                                                /                                                                  C                                  D                                                                                            )                                                        2                                                                                              ]                                                                            1                    /                    2                                                                                                                          =                                                P                  max                                /                                  (                                                            1                      2                                        ⁢                    ρ                    ⁢                                          xe2x80x83                                        ⁢                                          U                      3                                        ⁢                    A                                    )                                                                                        Eq        .                  xe2x80x83                ⁢        5            
Equation 5 gives the maximum power the proposed airfoil can produce given its values for CL, and CD. For airfoil motion off-axis with the wind direction (tether axis and wind direction are not aligned), power loss will result. For this discussion we have chosen reasonable numbers for the lift and drag coefficients, namely, CL≈1.0 and CD≈0.1. Substituting these into Equation 5 we get:                                                                         P                out                            =                                                C                  P                                ⁡                                  (                                                            1                      2                                        ⁢                    ρ                    ⁢                                          xe2x80x83                                        ⁢                                          U                      3                                        ⁢                    A                                    )                                                                                                        =                                                14.85                  ⁢                                      xe2x80x83                                    ⁢                                      (                                                                  1                        2                                            ⁢                      ρ                      ⁢                                              xe2x80x83                                            ⁢                                              U                        3                                            ⁢                      A                                        )                                    ⁢                                      xe2x80x83                                    ⁢                  at                  ⁢                                      xe2x80x83                                    ⁢                                      v                    /                    U                                                  =                7.00                                                                        Eq        .                  xe2x80x83                ⁢        6                                                                                    P                max                            =                                                C                                      P                    ,                    max                                                  ⁡                                  (                                                            1                      2                                        ⁢                    ρ                    ⁢                                          xe2x80x83                                        ⁢                                          U                      3                                        ⁢                    A                                    )                                                                                                        =                                                14.98                  ⁢                                      xe2x80x83                                    ⁢                                      (                                                                  1                        2                                            ⁢                      ρ                      ⁢                                              xe2x80x83                                            ⁢                                              U                        3                                            ⁢                      A                                        )                                    ⁢                                      xe2x80x83                                    ⁢                  at                  ⁢                                      xe2x80x83                                    ⁢                                      v                    /                    U                                                  =                                  6.67                  ⁢                                      xe2x80x83                                    ⁢                                      (                                                                  (                                                  2                          ⁢                                                      /                                                    ⁢                          3                                                )                                            ⁢                                              L                        /                        D                                                              )                                                                                                          Eq        .                  xe2x80x83                ⁢        7                                                                                    P                out                            =                                                C                  P                                ⁡                                  (                                                            1                      2                                        ⁢                    ρ                    ⁢                                          xe2x80x83                                        ⁢                                          U                      3                                        ⁢                    A                                    )                                                                                                        =                                                14.60                  ⁢                                      xe2x80x83                                    ⁢                                      (                                                                  1                        2                                            ⁢                      ρ                      ⁢                                              xe2x80x83                                            ⁢                                              U                        3                                            ⁢                      A                                        )                                    ⁢                                      xe2x80x83                                    ⁢                  at                  ⁢                                      xe2x80x83                                    ⁢                                      v                    /                    U                                                  =                6.00                                                                        Eq        .                  xe2x80x83                ⁢        8            
Notice that in equations 6 through 8 the power output is relatively insensitive to the actual ratio of airfoil velocity (v) to wind velocity (U). This is good since the airfoil speed will be relatively difficult to maintain exactly. Also notice that (xc2xdxcfx81U3A) is the standard power equation for a fluid flow passing through an area A. Thus, our hypothetical airfoil can effectively collect almost 15 times the energy in the wind passing through the projected area of the airfoil, or almost 40 times the power of a standard wind turbine (38% efficiency) with a sweep area equal to the airfoil area, or 150 times the energy collected by a simple drag collector. We have chosen the lift-to-drag ratio equal to 10, which is much lower than most standard wind turbine airfoils which have lift-to-drag ratios greater than 20:1. If higher tolerances can be met, higher airfoil kite speeds could be achieved which would produce more power for a given size airfoil. For example, if the Lift-to-Drag ratio is increased to 15, then the power output increases to 50.25 (xc2xdxcfx81U3A). This power output is approximately 200 times greater than the best windmills using a drag sail or airfoil that interacts with the air at the ambient wind speed, such as, U.S. Pat. Nos. 3,924,827 and 4,076,190 to Lois, U.S. Pat. No. 4,124,182 to Loeb, and U.S. Pat. No. 6,072,245 to Ockels. The high-speed tacking of the Applicant""s airfoil kite is what allows this high power rating and is a direct result of the airfoil interacting with a much larger volume of moving air.
From the example above we can see that small increases in the airfoil LIFT-to-DRAG ratio can greatly increase the total power output of the airfoil. Likewise, extra drag on the airfoil greatly reduces the total power output. Dirt on the airfoil and air drag on the control lines effectively reduces the LIFT-to-DRAG ratio of the kite by increasing the total drag on the system. Luckily, these drag forces become less and less of a factor as the system is scaled to larger sizes.
Let us now examine the power output of a hypothetical 1.33 meter by 7.5 meter airfoil (see FIG. 18 for a force diagram for this airfoil, and Table 1 for power data). The air density will be set at 1.0 kg per cubic meter (approx. 6,000 feet altitude), at lower altitudes more power is produced for the same wind speed. In this example, the airfoil""s aerodynamic shape has medium surface tolerances to produce a LIFT-to-DRAG ratio of 10 (L/D=10 taking into account drag induced by the control lines, support lines, and other supports, which effectively reduce L/D to 10). Its efficiency at collecting wind energy will be estimated at 29% as calculated in Eq. 12 and Eq. 13. We will also choose its operating speed at 6 times the ambient wind speed which is near the optimum power producing speed for an airfoil with a lift-to-drag ratio of 10 (note that the chosen operating speed is slightly below the optimum 6.67 times wind speed). Even with this rather small inefficient airfoil, we still obtain an impressive amount of power from the system. The airfoil produces its maximum rated pull (AXIAL force) at an ambient wind speed of only 12 m/s. Above 12 m/s wind speed the airfoil would need. to be throttled down to prevent damage to the kite. This is done in at least two ways. First, one can change the airfoil""s pitch angle so its LIFT is effectively reduced. By this method, the power output of the airfoil can be held relatively constant up to and above 100 mph winds at which point the airfoil will have a more difficult time compensating for the extra power. Second, the airfoil can be xe2x80x9cthrottledxe2x80x9d by simply increase the rate at which the control lines are reeled out. By increasing the reel-out rate, the effective wind speed is reduces and so are the forces associated with the airfoil and control lines. This faster reel-out of the lines also has the advantage of increasing the power output for the same maximum line tension. Thus, power output can still be increased as wind speed increases as long as the ground station components (pulleys, transmission, generator, etc.) can handle the extra power.
Two separate winds speeds are shown in Table 1, the wind speed at a height of 5 meters above the ground, and then the typical wind speed one would expect at an elevation of 250 meters. In studies it has been found that on average the wind speed at 250 meters is twice the wind speed at 5 meters elevation. The wind speed difference is the result of drag effects near the Earth""s surface where of objects on the ground (trees, houses, etc.) slow the wind down. As the airfoil kite exerts force on the control lines and the control lines are reeled-out (extended), it produces useful power which can then be converted into electrical power. Since the kite is moving at approximately 6 times the wind speed, the airflow it interacts with has 216 times the energy density of the ambient wind, and 1728 times the energy density of the ambient wind near the ground. Consequently, a very small airfoil can collect a very large amount of energy from this airflow. Not all the energy collected by the airfoil kite can be converted to useful work because there will be losses in the conversion process which includes the stopping of power output while the airfoil kite rewinds. We will calculate the Electrical Power Output as 29% of the Total Airfoil Power as determined in Eq. 13. For a wind speed of 12 m/s (27 mph), the kite shown in Table 1 is producing 126,144 watts of power, and has an average electrical output of 36,582 watts after taking into account all losses. During the power stroke at 12 m/s wind speed (8 m/s relative wind speed), the control lines would be extending at about 4.0 m/s, and be rewound at nearly twice that speed. As wind speed increases to 20 m/s, the relative wind speed on the airfoil stays at 8 m/s while the reel-out speed increases to 12 m/s. The flight speed and forces on the airfoil are substantially the same as at 12 m/s wind speed, but because the reel-out speed is 3 times greater for 20 m/s wind, the power output is 3 times greater.
Since the Linear Turbine converts its linear power into output power by playing out the tether during its power stroke, the output power for the system is determined by the force exerted while the lines are being played out and the speed at which they are being pulled out.
Power=Work/xc2x7time=Forcexc2x7Distance/Timexe2x80x83xe2x80x83Eq. 9
Distance divided by Time equals speed. So the Power produced by a line being pulled out is simply:                                                         Power              =                              Tension                ⁢                                  xe2x80x83                                ⁢                on                ⁢                                  xe2x80x83                                ⁢                                  line                  ·                  Reel                                ⁢                                  -                                ⁢                out                ⁢                                  xe2x80x83                                ⁢                Speed                                                                                        =                              AXIAL                ⁢                                  xe2x80x83                                ⁢                                  Force                  ·                                      (                                          1                      /                      3                                        )                                                  ⁢                Wind                ⁢                                  xe2x80x83                                ⁢                velocity                                                                        Eq        .                  xe2x80x83                ⁢        10            
If we assume that the AXIAL force is approximately equal to the LIFT on the airfoil, and we assume the relative air velocity is equal to the airfoil speed then we get an approximate expression for the Power output in terms of the wind speed (U):                                                         Power              =                                                1                  2                                ⁢                ρ                ⁢                                  xe2x80x83                                ⁢                                  V                  r                  2                                ⁢                                  C                  L                                ⁢                                  A                  ·                                      (                                          1                      /                      3                                        )                                                  ⁢                U                                                                                        =                                                1                  2                                ⁢                                                      ρ                    ⁡                                          (                                              6.67                        ⁢                                                  V                          w                                                                    )                                                        2                                ⁢                                  C                  L                                ⁢                                  A                  ⁡                                      (                                          1                      /                      3                                        )                                                  ⁢                U                                                                                        =                              7.41                ⁢                ρ                ⁢                                  xe2x80x83                                ⁢                                  C                  L                                ⁢                                  AU                  3                                                                                                        =                              14.8                ⁢                                  (                                                            1                      2                                        ⁢                    ρ                    ⁢                                          xe2x80x83                                        ⁢                                          C                      L                                        ⁢                                          AU                      3                                                        )                                                                                        Eq        .                  xe2x80x83                ⁢        11            
Where,
U=Wind speed
Vr=Relative air speed
xcfx81=air density
A=airfoil area
CL=Lift coefficient
Notice that this value is slightly below the numbers calculated in Eq. 7 because of the error in the two assumptions we made: 1) AXIAL force is actually slightly larger than LIFT force used in the calculation, and 2) the Relative Air Speed is slightly higher than the airfoil speed because it is the sum of the airfoil speed and wind speed vectors. Thus, Eq. 11 is only approximate, but give a better physical feel for how energy is generated by the airfoil and transmitted through the cables. Note, that this power output only occurs during the power stroke of the kite and the average power is much lower because of losses, and nonproductive rewind times.
The operation and control of airfoils are well known, and the determining of the proper angle-of-attack and pitch angle for the airfoil to maximize power output is straight forward as calculated above in equations: 1 through 11. However, under conditions of varying wind speed, and airfoil speed, calculating the proper angle becomes more difficult and the discussion of these more exact equations is beyond the scope of this application, but such equations are well known in the field of aerodynamics and wind turbine power.
Losses
As with any system, the Linear Wind-Turbine will have losses that reduce output power. Each loss will be given a coefficient of efficiency that can be used to calculate the net power output by multiplying them together. The major losses can be broken down into seven areas:
1) Cxcex8=Cos3(xcex8)=0.65 Losses from off-axis alignment of the airfoil with the wind direction. The wind strikes the airfoil at an angle effectively reducing the apparent wind speed, and since power is proportional to the cube of wind velocity we used Cosine cubed to determine the losses (Cxcex8=0.65 represents a value xcex8=30 deg). Thus, the collectable power is reduced by the cube cosine of the off-axis angle.
2) Cdrag=0.90 Losses from drag induced by the tether and control line. Losses here are small because drag on the lines can be minimized by making the Linear turbines larger.
3) Crewind=0.90 Losses from energy needed to rewind the tether after power stoke. In order to rewind the airfoil, power must be used. With a high-efficiency airfoil the rewind force can be hundreds of times less than the power stroke tension, but will still require an electric motor or other device to power the rewind.
4) Cdown=0.68 Losses due to time needed to rewind the tether (effects average power). Because no power is produced during the rewind phase this effectively lowers the average power output of the system
5) Ctrans=0.95 Losses within the pulley and transmission. Since the pulley and generator could be attached directly this loss can be very small. If a step-up transmission is needed this coefficient could increase to 0.85.
6) Cgen=0.85 Losses within the generator and power conditioning equipment. Any generator will have losses, however, if an asynchronous generator are used additional power converters will be needed to convert the non-matched current to the 60 Hz standard found on the US national power grid.
7) Airfoil DRAG lossesxe2x80x94*Note that losses due to drag on the airfoil are taken into account in Pmax (and Pout) from the Power equations (Eq. 5 through Eq. 8). The fact that the airfoil operates while the control lines are let out reduces the effective wind speed which is taken into account in the calculation of Pmax (and Pout).
Thus, the equation for maximum net output power is:
Pnet max=[Cxcex8CdragCrewindCdownCtransCgen]Pmaxxe2x80x83xe2x80x83(Eq. 12
If we assume an average xcex8=30 deg. (Cosine cube average), and non-ideal operating speeds of the airfoil, then the total net average power would be given by:                                                                         P                net                            =                                                [                                                            (                      0.65                      )                                        ⁢                                          (                      0.90                      )                                        ⁢                                          (                      0.90                      )                                        ⁢                                          (                      0.68                      )                                        ⁢                                          (                      0.95                      )                                        ⁢                                          (                      0.85                      )                                                        ]                                ⁢                                  P                  out                                                                                                        =                              0.29                ⁢                                  P                  out                                                                                        Eq        .                  xe2x80x83                ⁢        13            
Equation 13 shows that nearly 30% of the available power from the airfoil kite can be collected as useful electrical energy by this method of repetitive power-stroke and rewind. It should be noted that the time needed by the Applicant""s airfoil to rewind itself after each run is the second largest loss to average power output for the system (32% of time spent rewinding the control lines). This is conservative since airfoils have very low drag when pointed directly into the wind, which means it can be rapidly rewound using a minimum amount of force. With a faster rewind speed the Cdown loss can be decreased, thus directly resulting in greater average energy production. However, as rewind speed increases so does the power requirement for the rewind, thus Crewind loss will increase as rewind speed increases, but the losses due to rewind are small compared to the power gained by having the airfoil spend more time in a power stroke (at least to a point).
The system drag loss (Cdrag due to the control cables (tethers) has been estimated at 10%. As the airfoil systems get larger this drag component becomes less and less of a factor because air resistance on a cable goes up linearly with its diameter while the strength of the cable increases with the square of its diameter. This factor (Cdrag) also takes into account other drag losses such as those due to the airfoil curvature changes in flight, dirt on the airfoil (lowers lift-to-drag ratio), and flutter. DRAG on the control lines creates a force resisting the THRUST generated by the airfoil. This DRAG effectively reduces the lift-to-drag ratio of the airfoil kite and thus reduces the flight speed which reduces the power produced.
Operational Parameter
An airfoil generates the most power when it travels perpendicular to the wind (control lines parallel to the wind). When it moves away from this aligned state by rising into the sky, or flying horizontally, the wind strikes the airfoil at an angle. The greater the angle, and the less power the airfoil can generate. This loss can be attributed to a reduction in the effective wind speed, which is approximated by the Cosine of the angle {Veff=U Cos (xcex8)}, where xcex8 is the angle between the control line force vector at the airfoil and the wind direction. From this simple equation we can see that the airfoil power will be proportional to xe2x80x9cCos(xcex8) cubedxe2x80x9d because the power is proportional to the effective wind velocity cubed. The power generation factor Cos3(xcex8) is an approximation because it does not take into account such things as direction of airfoil flight, deformation of the airfoil, changes in L/D ratio, and other factors which have a small effect on a well designed airfoil kite. Note that the 36.5 kW airfoil (at 12 m/s wind) in Table 1, already assumes operation at xcex8=30 degrees (cube average) within the estimated 29% efficiency. At first glance this loss in power seems to greatly handicap the system as it would a standard wind turbine which does not track the wind properly. However, for a Linear Turbine the actual disadvantage is very small for two reasons. First, for high-elevation flight, the airfoil control lines will need to be angled at around 30 degrees with respect to the ground. The airfoils can operate at much lower angles, but because wind speed increases with height, it is actually an advantage to collect power at higher elevations. Second, it is easy, and relatively inexpensive, to add more airfoils to the system to bring the system back up to power, without upgrading the Power Platform, control lines, or generator. The loss of LIFT due to off-axis orientation is compensated for by simply having more airfoils.
Adverse Conditions
Hail, Snow, Rain, and Freezing Rain are potential problems for a Linear Turbine. The control lines are not easily damaged by hail, and snow and freezing rain would have a hard time collecting on the lines because of the dynamic nature of the their operation. Vibrations, bending and stretching all would tend to shake off any precipitation that would collect on them. If freezing rain or ice should become a problem the flexible nature of the airfoils and the ability to precisely control the flight path and speed of the airfoils allows a simple solution. The airfoils can simply be put into a controlled dive and crash into the ground at 20 to 30 mph without damaging the pliable airfoils. The impact would be more than enough to shake loose any snow or ice from the flexible slick plastic surface. Non-absorbent control-lines would aid in limiting the loading effects caused by snow, rain and freezing rain. The airfoil itself would need to have a reinforced leading edge to protect it from hail damage. The airfoil must also have a slick outside coating to allow vibrations and stretching of the fabric to dislodge any snow or freezing rain that might collect. The slick, high-puncture resistant, multi-layer material used to make modem white-water rafts seems perfect for this use. The material would be very durable and air tight allowing the inflation and pressurization of the airfoil with lighter-than-air gasses. It may be necessary to cover this entire structure with a thin flexible membrane which can expanded from time to time with air pressure; heating elements are also a possibility. A completely sealed and pressurized airfoil seems like the only workable kite system that could be make relatively maintenance free and still be lighter-than-air, and resist the elements. Also, during the winter season the entire system may need to be sprayed with Teflon or oil once a month to improve the removal of ice and snow.
Heavy Winds pose only minor problems for this wind system because of its normal operating speed above 120 mph. Through proper control of the airfoil""s angle-of-attack, pitch angle, reel-out line speed, and angle above the horizon, there is little problem keeping the airfoil producing power well above 100 mph wind speeds. Turbulence at these high wind speeds may require one-board systems to make very fast adjustments to the airfoil""s LIFT to prevent damage to the airfoil and lines. All these problems can be overcome simply by increasing the rate at which the airfoil is reeled-out during the power stroke. Increasing the reel-out speed reduces the effective wind speed the airfoil xe2x80x9cseesxe2x80x9d. Thus, the relative wind speed can be maintained below its maximum static wind speed even in very high wind conditions, provided the pulley system and generators can withstand the increased rate of line reel-out. Throttling the airfoil in this way has another advantage, which is the airfoil generates much more power because of the increased line speed without additional stress on the airfoils or control lines. The combination of increasing Cosine cubed losses, increasing line reel-out rate, and reducing angle-of-attack (and/or pitch angle) of the airfoil combine to provide good control over the airfoils even in very violent wind storms.
Lack of Sufficient Wind to keep the airfoils aloft, and turbulent wind conditions where angle-of-attack is constantly changing cause problems. These problems can be handled with proper line and tensioning control, which would reel the airfoils in when the wind stopped. Also, because the airfoils have no other components on them, it is possible to make them buoyant with lighter-than-air gasses. Thus, even if the wind stops the airfoil kite does not need to be reeled in.
Ultraviolet Radiation from the sun is another potential problem. The outer surface of the airfoil as well as the cables must be able to resist this damaging radiation. Materials that deteriorate in sunlight must be avoided or coated with a ultraviolet resistant material. For the cables stainless steel piano wire or carbon fiber cables might be used. If more exotic cabling is desired the cables can be coated to protect them. For the airfoil, a simple exterior coating would be all that is needed to protect the high strength plastic.
Turbulent Air can also cause problems. Since the airfoils are essentially high-speed kites, there is always the chance of the lines getting tangled. To prevent this several measures can be taken. First, as heavier and heavier control lines are used on larger and larger systems, it becomes less likely the lines will be to accidentally twisted since the size of the systems mean much slower reaction times are needed from the automated control systems. Second, the airfoils are not passively inflated like many para-foil kites are by air-ram effect. Instead, the applicant""s is inflated and pressurized so that they hold their shape even under strong forces. Third, active tensioning of the control lines keeps a minimum tension on the lines. If tension drops below a certain level, the airfoils are reeled in to prevent tangling of the lines. Forth, airfoils can be chained together in tandem to provide added stability. If one airfoil should loose lift due to turbulence the others can keep the train of airfoils under control (see FIG. 3). Fifth, the connectors between airfoils in, tandem are made semi-rigid so that the train of airfoils retain their shape even without active lift. In FIG. 3 we see two airfoils 50 in tandem with more airfoils attached above them. Connectors 56 and 64 are used to connect the airfoils together (note only left side of drawing is numbered, and the right side is the mirror image of the left side). If connectors 56 and 64 are made of a carbon fiber rod (slightly curved to dissipate compressive forces), then the airfoils will not only resist being forced apart but also resist being pushed together, or twisting around each other. Thus, making connectors 56 and 64 semi-rigid helps prevent the airfoils from getting tangled.
Lightning is the final hazard presented here. For large systems this is not a problem, as the Cable and Control Lines could be made of wire cables large enough to be undamaged by the flow of electricity caused by lightning. For smaller systems it may be necessary to bring them down during lightning storms. However, the use of non-conductive, water-repellant lines combined with the fact that the control lines are substantially horizontal to the ground may prevent lightning strikes from being a problem. Conversly, lightning rods and conduction paths on the airfoil kite itself could also be used to prevent damage.
Commercial/Economic Potential
According to the US World Atlas over half of the US land area has a power density greater than 200 W/m2 at a height of 50 meters (5.6 meters/second). At 250 meters one can expect the power density to be over 2 times this (depending on local terrain), with an equivalent average wind speed of Uave=7.3 meters per second. If ocean areas are considered we find that much of the open seas experience 500 W/m2 or more and represents the majority of the wind energy on the planet. For an example of a workable system, we will use four(4), 1.33 meter chord by 7.5 meter length airfoils in tandem. The estimated output power from this system at Uave=7.3 m/s is 8,450 watts, Pout=(0.29)[14.98(xc2xdxcfx81U3A)], for each of the four airfoils for a total of 33.8 kW(kilowatts). These numbers take into account all the losses as shown in equation 12. Since power increases with the cube of wind speed, there is much more energy above this average wind speed than below, with 3 to 4 times more energy available above Uave even though such velocities are experienced less often. Thus, the actual average power output will be greater than the power at Uave. For a typical wind speed distribution, the maximum Energy Density Frequency {(kWh/yr)/(m/s)} will occur at a wind velocity of approximately 150% of Uave. When averaged out over a year it is experimentally found that average power is approximately 141% of the power at Uave (for Uave above 100 m elevation). This means that the four tandem airfoils will output 47.6 kilowatts on average, or 417,000 kWh per year. The airfoils themselves will have a maximum power of 150 kW, but for economic reasons, the Power Platform, control lines, control systems, and generator will all be matched to half this value, or 75 kW (4 airfoils), for the maximum rating. This effectively lowers the wind speed at which maximum power is reached from 12 to 9.5 m/s, and gives the system an estimated annual capacity factor of 41.2 percent. Even more power can be produced if we take into account increased power output at higher winds speeds by reeling out the line at higher speeds to maintain safe stress levels on the airfoil and lines. However, for this example, the airfoil""s pitch angle is reduced to limit power output to the maximum rating 75 kW.
The 417,000 kWh/yr if sold at $0.05 per kilowatt-hour would return $20,850 per year. An initial break-even construction cost of $108,593 (not including interest during construction, inflation, variable annual costs, and taxes) would result if constructed with a 15 year-8% interest loan, and $5,000 per year operation and maintenance costs. The total capital costs of this small 4-airfoil Linear Turbine is estimated at only $48,000. The cost breakdown would be as follows: Airfoilsxe2x80x94$1,000 apiece when mass produced, and weigh less than 15 pounds (not including lift due to lighter-than-air gases). Power Platformxe2x80x94$6,000 and built to last a decade or more, with precision sealed bearings and heavy construction. Control Linesxe2x80x94$2,000. Control linkage in Ground stationxe2x80x94$10,000 and would be computer controlled. Computer controllerxe2x80x94$8,000, the computer controller and program would be one of the most expensive components to develop. Variable Speed 80 kW DC Generatorxe2x80x94$8,000, Power Grid Controller 80 kWxe2x80x94$6,000 for matching 60 Hz AC grid output (note that multiple airfoils operating in sequence to even out power could allow a constant-speed synchronous generator to be used, thus eliminating expensive electric power conditioning equipment). Finally, a small block house will be needed to house the generator and control systems at a cost of $3,000. At a total cost of $48,000, this works out to $1008 per average kilowatt output ($414 per installed peak kW, 41% utility), in a wind zone on the low end of a Class 2 site (average wind speeds from 5.6 to 6.4 m/s at 50 meter elevation). With $5,000/yr operational costs, $3,840/yr interest (8%), and $3200/yr principle, a kilowatt-hour of electricity would cost $0.017/kWh ($7040/417,000 kWh) for capital costs, and $0.012/kWh ($5000/417,000 kWh) for maintenance and replacement. This provides a total cost of $0.029/kWh. Present wind system have capital costs as low as $1,050 per kW ($0.03/kWh capital costs, and $0.01/kWh operating costs)1 with a utility factor around 30%. In non-ideal wind zones these present day wind systems would produce electricity at $0.075 to $0.083 per kWh. Thus, this proposed system has approximately the same capital cost of the best wind farms, while operating at a higher utility factor, in a location with only one-half the wind energy density available, and accomplishes this in a very small sized system. As linear turbine systems are scaled to larger sizes the economics get even better. Thus, with such a low cost per kilowatt-hour, a Linear Turbine appears capable of competing economically with nearly any other form of energy, even with maintenance and replacement costs representing more than half of the cost of the system.
One final note: The Applicant purchased an airfoil kite to conduct experiments on this type of wind power generation. The small 7 foot long airfoil kite weighed only 8 ounces, but could operate at power levels above 8 horsepower without damage. That is, it can deliver 8 hp to the control lines on the ground in normal operation (40 mph wind speed, 20 feet/sec reel-out line speed, 220 pound line tension). This must be a record; the power output is an astounding 1 hp per ounce! I don""t know of anything other than a rocket or turbojet engine that can produce that kind of power-to-weight ratio. If a typical 100 hp automobile engine had the same power-to-weight ratio it would weigh only 6 pounds (3 kg).
Scaling
Standard wind turbines suffer from bending moments which increase with the square of the blade length and blade thrust which increases linearly with blade length. Combining these two factors explains why there is problems with rotors more than 100 meters in diameter; forces increase beyond what material strength can support. Flexible airfoil kites do not suffer from this problem and actually require no increase in structural strength when scaling the length of the airfoil or scaling the number of airfoils in tandem, only the ground station and cabling need to be strengthened to handle the added power. The reason for this is that the airfoils can be divided into cells along its span(width) with each cell having its own support lines. This arrangement allows the airfoil to be made wider by adding more cells and lines without changing the forces acting on each cell. Power can also be increased by adding more airfoils in tandem which obviously does not increase the stress on the separate airfoils. Only the control lines, and ground station would need to be made stronger as power output increased. Increasing the chord of the airfoil, however, does require an increase in strength of the fabric the airfoil is made of. An airfoil""s chord is defined as the distance between its leading edge and its trailing edge. The forces on the material increase linearly with chord length, but this in itself does not impose a limitation on the system size, it just requires proportionally stronger materials for larger airfoil chords. Because it is a linear relationship, there is no absolute maximum size for such an airfoil chord. Airfoil sizes of 5 meter chord and 50 meter length are certainly possible, and if stacked in a train of 40, such a system would produce 20 MW (2,000 W/m2). Thus, at least on paper, Linear Wind-Turbines appear to be highly scalable to very large sizes.
Objectives of Advantages
Accordingly, several objects and advantages of my invention are:
a) This Turbine Kite system is able to reach high elevation air streams where higher velocity wind provides a much higher energy density than at the surface.
b) High elevation operation makes available the collection of energy from a much larger percentage of the total wind energy on Earth.
c) High speed operation allows a relatively small kite to collect a large amount of energy over a large volume of air.
d) Expensive components of the system remain on the ground and protected.
e) All heavy components of the system remain on the ground allowing buoyant airfoils to be used.
f) The airfoil acts like the tip of a normal rotor blade, the area of highest power generation, without the need for a large tower, expensive rotor hub and the rotor blades, which are all replaced with inexpensive control lines.
g) Very low center-of-gravity allows the system to easily be placed at sea.
h) The flight control system can be made insensitive to rocking and rolling of the ground station if placed at sea.
i) Quick and easy changing of buoyant kite trains for repair or inspection.
j) Continued operation even in extreme wind conditions above 100 MPH.
k) Production of power from the AXIAL component of LIFT.
l) Use of an inflated airfoil with lighter-than-air gas to provide buoyancy.
m) Use of semi-rigid spars between airfoil kites in tandem to prevent tangling and to keep the airfoils at the proper angle-of-attack even in turbulent wind.
n) To allow increase power output while at the same time reducing the stresses on the airfoil and control lines by reeling-out the control lines faster.
o) To provide a wind energy system which can be scaled to very high power levels.
p) To provide a single attachment point on the ground for the airfoil kites so that simplified flight controls can be used to control the airfoil""s flight path.
q) To provide airfoil pitch angle control which can maximizes the LIFT-to-DRAG ratio of the airfoil during the power stroke phase.